SOLUTION: Ok so we've got to write a polynomial function. r1=4, r2=5, and r3=6 (x-4)(x-5)(x-6)=0 (x^2)-5x-4x+20=0 ((x^2)-9x+20)(x-6) I'm stuck here. I hope it all makes sense.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Ok so we've got to write a polynomial function. r1=4, r2=5, and r3=6 (x-4)(x-5)(x-6)=0 (x^2)-5x-4x+20=0 ((x^2)-9x+20)(x-6) I'm stuck here. I hope it all makes sense.      Log On


   

Question 211171: Ok so we've got to write a polynomial function.
r1=4, r2=5, and r3=6
(x-4)(x-5)(x-6)=0
(x^2)-5x-4x+20=0
((x^2)-9x+20)(x-6)
I'm stuck here. I hope it all makes sense.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You're off to a great start. I'll start where you left off.


%28x%5E2-9x%2B20%29%28x-6%29=0 Start with the given equation.


%28x-6%29%28x%5E2-9x%2B20%29=0 Rearrange the terms.


x%28x%5E2-9x%2B20%29-6%28x%5E2-9x%2B20%29=0 Expand. Note: %28A%2BB%29%28C%2BD%2BE%29=A%28C%2BD%2BE%29%2BB%28C%2BD%2BE%29


x%28x%5E2%29-x%289x%29%2Bx%2820%29-6%28x%5E2%29-6%28-9x%29-6%2820%29=0 Distribute


x%5E3-9x%5E2%2B20x-6x%5E2%2B54x-120=0 Multiply


x%5E3-15x%5E2%2B74x-120=0 Combine like terms.


So %28x%5E2-9x%2B20%29%28x-6%29=x%5E3-15x%5E2%2B74x-120


This means that the polynomial with the roots r%5B1%5D=4, r%5B2%5D=5, and r%5B3%5D=6 is y=x%5E3-15x%5E2%2B74x-120